Consider a 1-D piece of silicon of length 1um. It is connected to a thin insulator...

 

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Consider a 1-D piece of silicon of length 1um. It is connected to a thin insulator (SiO2) of thickness 1nm on the left. Suppose there is an infinite energy barrier for carriers from silicon into the insulator. The right edge of silicon is connected to metal. The semiconductor is under constant uniform illumination due to which there are excess electrons and holes in it. Assume low level injection. Suppose the recombination lifetime in silicon is 100 sec. Assume carrier mobility of 1000 cm²V/s and T = 300K. Any other material parameters that are not given can be taken from textbook. (6) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) From the given energy band diagram, is there any electric field in silicon? Should there be any drift current for electron or holes in steady state? Write the minority carrier diffusion equation (MCDE) for holes in the silicon in steady state. Calculate diffusion length for holes. Compare it with the physical length of the device. Is it much shorter or much longer? Based on part (iv) argue whether it is appropriate or not to assume negligible recombination in silicon? Do appropriate simplifications in the MCDE that you wrote in part (iii). Write a general solution for the simplified MCDE that you wrote in part (vi). Assume excess carrier concentration to be 0 at x = L. Find out the excess hole concentration at x = 0. Use solutions of the previous parts to write an expression for the diffusion current for holes. Problem 1: [2+2+3+3+2+3+5+7+3+3+3+3+6=45] U=∞0 G = 10² / (m²³3) s) U=-a x=0 FP → -1M² |F= EN X=L Consider a 1-D piece of silicon of length 1um. It is connected to a thin insulator (SiO2) of thickness 1nm on the left. Suppose there is an infinite energy barrier for carriers from silicon into the insulator. The right edge of silicon is connected to metal. The semiconductor is under constant uniform illumination due to which there are excess electrons and holes in it. Assume low level injection. Suppose the recombination lifetime in silicon is 100 sec. Assume carrier mobility of 1000 cm²V/s and T = 300K. Any other material parameters that are not given can be taken from textbook. (6) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) From the given energy band diagram, is there any electric field in silicon? Should there be any drift current for electron or holes in steady state? Write the minority carrier diffusion equation (MCDE) for holes in the silicon in steady state. Calculate diffusion length for holes. Compare it with the physical length of the device. Is it much shorter or much longer? Based on part (iv) argue whether it is appropriate or not to assume negligible recombination in silicon? Do appropriate simplifications in the MCDE that you wrote in part (iii). Write a general solution for the simplified MCDE that you wrote in part (vi). Assume excess carrier concentration to be 0 at x = L. Find out the excess hole concentration at x = 0. Use solutions of the previous parts to write an expression for the diffusion current for holes. Problem 1: [2+2+3+3+2+3+5+7+3+3+3+3+6=45] U=∞0 G = 10² / (m²³3) s) U=-a x=0 FP → -1M² |F= EN X=L

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1 From the given energy band diagram i Yes there should be an electric field in silicon The presence ... View the full answer